The Production of Diffraction Gratings: II The Design of Echelle Gratings and Spectrographs1

In seeking to circumvent the difficulties that have limited production of ruled gratings having resolving powers in excess of 400,000, it is observed that resolving power at a given wave-length depends only on the ruled width of the grating and the angles of illumination and observation, and not specifically on the number of ruled grooves. The reflection echelon is a grating of high resolving power in which groove separation has been increased to a degree involving extreme sacrifice of free spectral range. It is suggested that much could be gained by producing a grating with only as many reflecting grooves per inch as are needed to give sufficient free spectral range to avoid difficulties arising from overlapping of orders. For the study of Zeeman effects, hyperfine structure, and complex atomic and molecular spectra, 20 wave numbers of free spectrum should suffice, which would require use of about 100 grooves per inch. Such gratings, having a simple step groove form that reflects light of all orders in a narrow bundle, and designed to be used at an angle of incidence greater than 45° and normal to the narrow side of the “step,” may be designated “echelles,” as intermediate in character between the echellette and the echelon. Echelles should lend themselves to production of very powerful compact spectrographs giving single-exposure coverage of broad spectral ranges. A 10-inch echelle having 1000 grooves of width 0.25 mm, each with one flat side 0.05 mm deep, gives at 5000A a theoretical resolving power of one million, a free spectral range of 5A and a plate factor of 0.2 A/mm, when used with a lens or mirror of only 250 cm focal length. It should thus be as powerful as a 10-inch concave grating of 42 ft. radius having 30,000 grooves per inch when used in the third order, and would be much faster even though used with a lens of less than 75 mm aperture. When crossed with a suitable prism or grating of low dispersion this echelle should, without overlapping of orders, produce spectrograms having a range of 10,000 wave numbers or more on a single plate, instead of the 5 to 25 plates required by the equivalent orthodox grating in the Paschen-Runge mount. The echelle spectrograph would also offer great gains in stability and portability. Problems and possibilities of the production of original and replica echelles are discussed, and it is shown that the reduction of ruling time from weeks to hours makes interferometric control of groove spacing in gratings appear feasible for the first time.